Morphisms of Skew Hadamard Matrices
Abstract
Quaternary unit Hadamard (QUH) matrices were introduced by Fender, Kharagani and Suda along with a method to construct them at prime power orders. We present a novel construction of real Hadamard matrices from QUH matrices. Our construction recovers the result by Mukhopadhyay on the existence of real Hadamard matrices of order qn+qn-1 for each prime power q 3 4. Furthermore we provide nonexistence conditions for QUH matrices.
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